Mark Twain visited Bermuda on eight separate occasions of various durations.  His first visit was from Monday, November 11 to Friday, November 15 of 1867, the final port of call of the Quaker City voyage, before returning to New York.   According to Rasmussen, this was not in fact his first visit.  He reports that the Quaker City stopped there on the way to the Azores in mid-June of 1867.

From Page 436-7 The Life of Mark Twain: The Early Years, 1835-1871:

Finally, on November 11, as Sam remarked, “the beautiful Bermudas rose out of the sea.” The Quaker City lay at anchor in the harbor of St. George, its last port of call, for four days, and Sam remembered them fondly, Though he supposed in retrospect that “we only stopped at the Bermudas because they were in the programme,” he discovered to his delight “civilization and intelligence” under the British flag “in place of Spanish and Italian superstition, dirt and dread of cholera.” Moses Beach thought the topography “little less than bewitching.” Duncan, who had scheduled the layover, was no less pleasantly surprised. “We expected nothing but a sand hill,” he noted in his log, “and found high ground, green foliage and fine scenery” with opportunities for “riding, driving, walking, sailing.” Surveying the islands with what Mary Louise Pratt has termed the “imperial gaze,” Mary Mason Fairbanks concluded that “a few years of energetic American persevering labor, such as clears our Western wilds, would make an Eden of the Bermudas.” On Wednesday evening, November 13, returning from dinner in St. George to the yacht about a mile from shore, she and a group of friends, including Moses and Emma Beach and Solon and Emily Severance, “experienced much difficulty in stemming the current. Our oarsmen tugged manfully” and Sam, the former steamboat pilot at the helm, “held the rudder with a strong hand, while the spray dashed over his Parisian broadcloth and almost extinguished his inevitable cigar.” It is the last reference to him recorded by any of the passengers before the Quaker City docked in New York on November 19, the same day Charles Dickens landed in Boston for his first American speaking tour since 1842.  ...
... Sam was the first person to disembark from the ship, and he was waved through customs.

The second trip, accompanied by his good friend the Reverend Joseph Twichell, was from  Sunday, May 20 to Thursday, May 24, 1877. This visit to the islands was the subject of a piece published in 1877, “Some Rambling Notes on an Idle Excursion”, written for the Atlantic magazine, Oct. to Jan. 1878. The voyage to Bermuda in the spring of 1877 greatly satisfied Clemens, just as the “Idle Excursion” pleased Howells at the Atlantic. “I’ve just been reading aloud to my wife your Bermuda papers,” Howells wrote on June 30. “That they’re delightfully entertaining goes without saying; but we also found that you gave us the only realizing sense of Bermuda that we’ve ever had.” Clemens had already written Twichell. “It was much the joyousest trip I ever had, Joe—not a heartache in it,” he said, “not a twinge of conscience.”  

Mark Twain’s fame inevitably benefited Bermuda, and the Islands gained further attention in 1883, when Princess Louise of Canada arrived for a winter respite. She was a daughter of Queen Victoria, and was grandly hailed as “the first real live Princess who ever gladdened Bermuda with her presence.” Princess Louise must have heard talk about Mark Twain. She stayed until April 10, and the next month she and her husband, the Marquis of Lorne, governor-general of Canada, entertained Clemens in Ottawa.

A new hotel named the Princess opened in Hamilton at the end of 1884. Bermuda was preparing for a larger number of tourists, most of them from the eastern seaboard. By 1890 the Islands were known as a haven for well-to-do Americans. Howells returned in 1901, and described Bermuda as a place “where time is so long that if you lose your patience you easily find it again.” Much like Clemens, he considered Bermuda a paradise—one that had an advantage over Eden. Apparently, it was not woman and her seed who were expelled, he wrote, but the serpent and his seed, for “women now abound in the Summer Islands, and there is not a snake anywhere to be found.”

At year’s end, the New York Herald published a guide to winter resorts. The beauties of Bermuda, the paper said, were immortalized by the poet Tom Moore, and Mark Twain—“as much poet as humorist”—had added his tribute:   And now the Bermuda season is already in full swing. The Quebec steamship line already has so large a booking that it may be compelled to put another steamer in this particular service during the height of the season. The big, roomy twin screw steamer Bermudian, which was built specially to meet the demands of increased travel and placed on the line two seasons ago, accommodates 238 first class passengers. . . .   

Bermuda has developed into an all year resort. . . . Last summer from 1,500 to 2,000 excursionists visited the place, an increase of forty per cent over last year. Five years ago no one visited the resort during the summer months. . . .   A stranger floating over the white shoals of a coral reef for the first time will be wonderstruck by the marvellous clearness of the sea water and the strange effect of deception as to depth. Objects which appear to reach nearly to the surface are found to be so deep that the vessel passes safely over them. The sunlight reaches many fathoms down. . . . And the color—that beautiful bewildering green, just the shade that one catches in the gleam of an opal or the tint of a malachite. Painters have sought in vain to rival it with their pigments.   

Clemens, Twichell, and Miss Lyon sailed on Wednesday, January 2, 1907. The trip now took two days rather than three. The third trip was January 4 - 7, 1907.  Twain was accompanied by Reverend Twichell and his secretary Isabel Lyon. The fourth trip was from Saturday, March 16 to Tuesday, March 19, 1907, accompanied by Miss Lyon and Angelfish Paddy Madden. The fifth trip:  January 25 – February 3, 1908, accompanied by Ralph Ashcroft. January 25 Saturday – Sam left for Bermuda on the Bermudian. The New York Times, Jan. 26, p. 4 noted his departure and added: “Mr. Clemens has been ill at his home for some days, and when he arrived at the vessel went direct to his stateroom and did not emerge while the vessel was at her pier. He was ordered south by his physician because of an attack of laryngitis.”

January 26 Sunday – After traversing stormy seas, the Bermudian docked in Hamilton Harbor, Bermuda in the morning [D. Hoffman 89]. Note: The passage took 45 hours; Sam left shortly after a ten-inch snowstorm in NYC [A.D. of Feb. 12].  12 February 1908: Paragraph 12," in Autobiography of Mark Twain, Volume 3. 2015 [I have been to Bermuda again; this is the fifth time]; it was on account of bronchitis, my annual visitor for these seventeen or eighteen years. I have not come out of any previous attack so quickly or so pleasantly; the attack has always kept me in bed five weeks, sometimes six, and once eight. This time I got out of bed at the end of the first week, two days after a ten-inch snow-storm, and took the chances and went to sea in bitter winter weather. [We made the passage in forty-five hours and landed in lovely summer weather. The passage itself came near to curing me, for a radical change is a good doctor. A [single day] of constant and delightful exposure to the Bermudian sun completed the cure; then I stayed [eight] days longer] to enjoy the spiritual serenities and the bodily [rejuvenations] furnished by that happy little paradise. It grieves me, and I feel reproached, that [I allowed the physicians to send Mrs. Clemens on a horrible ten-day sea journey to Italy] when Bermuda was right here at hand and worth a hundred Italies, for her needs. They said she must have a warm and soft and gentle climate, and that nothing else could help her. The winter climate of Florence distinctly failed to meet the requirements; we had eight months of uncomfortable weather, with much chilliness, two months of rain, and very infrequent splashes of sunshine. She was not able to outlive these disasters, and she was never able to flee from them, for lack of strength. It astonishes me and grieves me to remember that when Italy was proposed Bermuda never once occurred to me; yet I knew Florence well, and I knew Bermuda well, and was aware that for climate Florence was a sarcasm as compared with Bermuda.

The sixth trip:  Monday February 24 to Saturday April 11, 1909.   Clemens returned to Bermuda and stayed much longer than ever before, forty-seven days. He traveled with his close friend Henry Huttleston Rogers, of the Standard Oil Trust; William E. Benjamin, who was Rogers’s son-in-law; the loyal Miss Lyon; and Rogers’s valet. He insisted that the trip was not for his own health, but to benefit Rogers. He noted in his autobiography: “It is as I said, I am not leaving for Bermuda to build up my health, for there is nothing the matter with it; I am going because a change of scene and climate is absolutely necessary for H. H. Rogers, and he won’t go unless I go too.”

When they sailed on February 22, Miss Lyon wrote that “Mr. Rogers came feebly onto the boat, a sick, sick man.” H. H. (“Hell Hound”) Rogers was a multimillionaire commonly considered a ruthless predator. He admired Mark Twain’s book Roughing It, and once said, “As the man who sold two-cent cigars at sixty cents apiece in his shack in the middle of the alkali desert remarked: ‘We are not in business for our health.’” But now his health indeed had failed; he suffered a stroke in July 1907. Rogers had begun to manage Clemens’s financial affairs in 1893. Although his time was worth thousands of dollars a day, said the World’s Work, he served Clemens entirely in friendship, guiding him out of bankruptcy into substantial new wealth. Ambivalent in his attitude toward the very rich, Clemens joked about the “Standard Oiligarchy” and recalled how much cod-liver oil he had been fed as a child, saying, “I was the first Standard Oil Trust.”

Seventh Trip:  November 22 to Saturday December 18, 1909, with Albert Bigelow Paine. Eighth Trip:  Friday January 7 to Tuesday April 12, 1910, with Claude Benchotte, his valet.